Multiplication and Area - Ms. vecore's third grade...3•Lesson 2 Homework 4 Lesson 2: Decompose and recompose shapes to compare areas. Name Date 1. Each is a square unit. Count to

GRADE 3 • MODULE 4Multiplication and Area

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Homework

3 G R A D E Mathematics Curriculum

GRADE 3 • MODULE 4

Module 4: Multiplication and Area i

Table of Contents

GRADE 3 • MODULE 4 Multiplication and Area Module Overview ......................................................................................................... i Topic A: Foundations for Understanding Area ...................................................... 4.A.1 Topic B: Concepts of Area Measurement ............................................................... 4.B.1 Topic C: Arithmetic Properties Using Area Models................................................. 4.C.1 Topic D: Applications of Area Using Side Lengths of Figures .................................. 4.D.1 Module Assessments ............................................................................................. 4.S.1

NOTE: Student sheets should be printed at 100% scale to preserve the intended size of figures for accurate measurements. Adjust copier or printer settings to actual size and set page scaling to none.

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Lesson 1 Homework 3•4

Lesson 1: Understand area as an attribute of plane figures.

Name Date

1. Magnus covers the same shape with triangles, rhombuses, and trapezoids.

a. How many triangles will it take to cover the shape?

b. How many rhombuses will it take to cover the shape?

c. Magnus notices that 3 triangles from Part (a) cover 1 trapezoid. How many trapezoids will you need

to cover the shape below? Explain your answer.

_______ triangles

_______ rhombuses

_______ trapezoids

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3© 2014 Common Core, Inc. All rights reserved. commoncore.org





Lesson 1: Understand area as an attribute of plane figures.

2. Angela uses squares to find the area of a rectangle. Her work is shown below.

a. How many squares did she use to cover the rectangle?

b. What is the area of the rectangle in square units? Explain how you found your answer.

3. Each is 1 square unit. Which rectangle has the biggest area? How do you know?

_______ squares

Rectangle A

Rectangle B

Rectangle C

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Lesson 2: Decompose and recompose shapes to compare areas.

Name Date

1. Each is a square unit. Count to find the area of each rectangle. Then, circle all the rectangles with an area of 12 square units.

a. b. c.

d. f. e.

Area = _______ square units






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Lesson 2: Decompose and recompose shapes to compare areas.

2. Colin uses square inch pieces to create these rectangles. Do they have the same area? Explain.

3. Each is a square unit. Count to find the area of the rectangle below. Then, draw a different rectangle that has the same area.

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Lesson 3: Model tiling with centimeter and inch unit squares as a strategy to measure area.

Name Date

1. Each is 1 square unit. What is the area of each of the following rectangles?

A: square units

B: __________________

C: __________________

D: __________________

2. Each is 1 square unit. What is the area of each of the following rectangles?

A

B

C

D

a. b.

c. d.

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Lesson 3: Model tiling with centimeter and inch unit squares as a strategy to measure area.

3. Each is 1 square unit. Write the area of each rectangle. Then, draw another rectangle with the same area in the space provided.

A

Area = ___________________ square units

B

Area = _____________________________

C

Area = _____________________________

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Lesson 4: Relate side lengths with the number of tiles on a side.

Name Date

1. Ella placed square centimeter tiles on the rectangle below, and then labeled the side lengths. What is the area of her rectangle?

Total area: ________________________

2. Kyle uses square centimeter tiles to find the side lengths of the rectangle below. Label each side length. Then, count the tiles to find the total area.

Total area: ________________________

3. Maura uses square inch tiles to find the side lengths of the rectangle below. Label each side length. Then, find the total area.

Total area: ________________________

2 cm

4 cm

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Lesson 4: Relate side lengths with the number of tiles on a side.

4. Each square unit below is 1 square inch. Claire says that the side length of the rectangle below is 3 inches. Tyler says the side length is 5 inches. Who is correct? Explain how you know.

5. Label the unknown side lengths for the rectangle below, and then find the area. Explain how you used the lengths provided to find the unknown lengths and area.

Total area: ________________________

2 inches

4 inches

_________________

_________________

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Lesson 5: Form rectangles by tiling with unit squares to make arrays.

Name Date

1. Use the centimeter side of a ruler to draw in the tiles, and then skip-count to find the unknown side length or area. Write a multiplication sentence for each tiled rectangle.

_______ × _______ = _______

4 cm

a. Area: 24 square centimeters.

4 24

_______ × _______ = _______

6 cm

b. Area: 24 square centimeters.

3 cm

d. Area: 15 square centimeters.

_______ × _______ = _______ _______ × _______ = _______

5 cm

c. Area: 15 square centimeters.

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Lesson 5: Form rectangles by tiling with unit squares to make arrays.

2. Ally makes a rectangle with 45 square inch tiles. She arranges the tiles in 5 equal rows. How many square inch tiles are in each row? Use words, pictures, and numbers to support your answer.

3. Leon makes a rectangle with 36 square centimeter tiles. There are 4 equal rows of tiles. a. How many tiles are in each row? Use words, pictures, and numbers to support your answer.

b. Can Leon arrange all of his 36 square centimeter tiles into 6 equal rows? Use words, pictures, and numbers to support your answer.

c. Do the rectangles in Parts (a) and (b) have the same total area? Explain how you know.

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Lesson 6 Homework 3 4

Lesson 6: Draw rows and columns to determine the area of a rectangle given an incomplete array.

Name Date

1. Each represents a 1 cm square. Draw to find the number of rows and columns in each array. Match it to its completed array. Then, fill in the blanks to make a true equation to find each array’s area.

f.

_____ × _____ = _____ sq cm

_____ × _____ = _____ sq cm

_____ × _____ = _____ sq cm

_____ × _____ = _____ sq cm

_____ × _____ = _____ sq cm

_____ × _____ = _____ sq cm

a.

b.

c.

d.

e.

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Lesson 6: Draw rows and columns to determine the area of a rectangle given an incomplete array.

2. Minh skip-counts by sixes to find the total square units in the rectangle below. She says there are 36 square units. Is she correct? Explain your answer.

3. The tub in Paige’s bathroom covers the tile floor as shown below. How many square tiles are on the floor, including the tiles under the tub?

4. Frank sees a book on top of his chessboard. How many squares are covered by the book? Explain your answer.

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Lesson 7: Interpret area models to form rectangular arrays.

Name Date

1. Find the area of each rectangular array. Label the side lengths of the matching area model, and write a

multiplication equation for each area model.

Rectangular Arrays Area Models

a.

b.

c.

______ square units

______ square units

______ square units

______ square units

d.

3

2

3 _____ = _____

_____ ______ = _____

_____ _____ = ______

_____ _____ = ______

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Lesson 7: Interpret area models to form rectangular arrays.

2. Jillian arranges square pattern blocks into a 7 by 4 array. Draw Jillian’s array on the the grid below. How many square units are in Jillian’s rectangular array?

a.

b. Label the side lengths of Jillian’s array from Part (a) on the rectangle below. Then, write a

multiplication sentence to represent the area of the rectangle.

3. Fiona draws a 24 square centimeter rectangle. Gregory draws a 24 square inch rectangle. Whose

rectangle is larger in area? How do you know?

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Lesson 8: Find the area of a rectangle through multiplication of the side lengths.

Name Date

1. Write a multiplication equation to find the area of each rectangle.

a. b.

c.

2. Write a multiplication equation and a division equation to find the unknown side length for each rectangle.

_______ × _______ = _______

_______ × _______ = _______

6 cm

8 cm

3 cm Area: ______ sq cm

8 cm

Area: ______ sq cm

_______ × _______ = _______

4 ft

4 ft

Area: ______ sq ft

d.

_______ × _______ = _______

4 ft Area: ______ sq ft

7 ft

_____ ft. a.

3 ft

_______ × _______ = _______

_______ _______ = _______

Area: 24 sq ft

9 ft b.

_____ ft

_______ × _______ = _______

_______ _______ = _______

Area: 36 sq ft

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Lesson 8: Find the area of a rectangle through multiplication of the side lengths.

3. On the grid below, draw a rectangle that has an area of 32 square centimeters. Label the side lengths.

4. Patricia draws a rectangle that has side lengths of 4 centimeters and 9 centimeters. What is the area of

the rectangle? Explain how you found your answer.

5. Charles draws a rectangle with a side length of 9 inches and an area of 27 square inches. What is the

other side length? How do you know?

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Lesson 9: Analyze different rectangles and reason about their area.

Name Date

1. Use the grid to answer the questions below.

a. Draw a line to divide the grid into 2 equal rectangles. Shade in 1 of the rectangles that you created.

b. Label the side lengths of each rectangle.

c. Write an equation to show the total area of the 2 rectangles.

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Lesson 9: Analyze different rectangles and reason about their area.

2. Alexa cuts out the 2 equal rectangles from Problem 1(a) and puts the two shorter sides together.a. Draw Alexa’s new rectangle and label the side lengths below.

b. Find the total area of the new, longer rectangle.

c. Is the area of the new, longer rectangle equal to the total area in Problem 1(c)? Explain why or whynot.

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Lesson 10: Apply the distributive property as a strategy to find the total area of a large rectangle by adding two products.


Name Date

1. Label the side lengths of the shaded and unshaded rectangles. Then, find the total area of the large rectangle by adding the areas of the 2 smaller rectangles.

a. b.

c. d.

9 × 12 = 9 × (______ + ______)

= (9 × ______) + (9 × ______)

= ______ + ______

= ______ square units

7 × 13 = 7 × (______+ 3)

= (7 × ______) + (7 × 3)

= ______ + ______


7

8

5

4

9 × 8 = (5 + 4) × 8

= (5 × 8) + (4 × 8)

= ______ + ______


5

2

12 × 5 = (______ + 2) × 5

= (______ × 5) + (2 × 5)

= ______ + 10


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Lesson 10: Apply the distributive property as a strategy to find the total area of a large rectangle by adding two products.


2. Finn imagines 1 more row of nine to find the total area of 9 × 9 rectangle. Explain how this could help him solve 9 × 9.

3. Shade an area to break the 16 × 4 rectangle into 2 smaller rectangles. Then, find the sum of the areas of the 2 smaller rectangles to find the total area. Explain your thinking.

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Lesson 11: Demonstrate the possible whole number side lengths of rectangles with areas of 24, 36, 48, or 72 square units using the associative property.

Name Date

1. The rectangles below have the same area. Move the parentheses to find the missing side lengths.

Then, solve.

2. Does Problem 1 show all the possible whole number side lengths for a rectangle with an area of 36 square centimeters? How do you know?

9 cm

4 cm

Area: 4 × ______ = ______sq cm a.

1 cm

36 cm

Area: 1 × 36 = ______ sq cm b.

______ cm

2 cm

Area: 4 × 9 = (2 × 2) × 9

= 2 × 2 × 9

= ______ × ______

= ______ sq cm

c.

______ cm

______ cm

Area: 4 × 9 = 4 × (3 × 3)

= 4 × 3 × 3

= ______ × ______

= ______ sq cm

d.

______ cm

______ cm

e. Area: 12 × 3 = (6 × 2) × 3

= 6 × 2 × 3

= ______ × ______

= ______ sq cm

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Lesson 11: Demonstrate the possible whole number side lengths of rectangles with areas of 24, 36, 48, or 72 square units using the associative property.

3. a. Find the area of the rectangle below.

b. Hilda says a 4 cm by 12 cm rectangle has the same area as the rectangle in Part (a). Place

parentheses in the equation to find the related fact and solve. Is Hilda correct? Why or why not?

c. Use the expression 8 × 6 to find different side lengths for a rectangle that has the same area as the

rectangle in Part (a). Show your equations using parentheses. Then, estimate to draw the rectangle

and label the side lengths.

6 cm

8 cm

4 × 12 = 4 × 2 × 6

= 4 × 2 × 6

= ______ × ______

= ______ sq cm

cm

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Lesson 12 Homework

3 4

Lesson 12: Solve word problems involving area.

Name Date

1. A square calendar has sides that are 9 inches long. What is the calendar's area?

2. Each is 1 square unit. Sienna uses the same square units to draw a 6 × 2 rectangle and says that it has the same area as the rectangle below. Is she correct? Explain why or why not.

3. The surface of an office desk has an area of 15 square feet. Its length is 5 feet. How wide is the office desk?

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Lesson 12 Homework

3 4

Lesson 12: Solve word problems involving area.

4. A rectangular garden has a total area of 48 square yards. Draw and label two possible rectangular gardens with different side lengths that have the same area.

5. Lila makes the pattern below. Find and explain her pattern. Then, draw the fifth figure in her pattern.

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Lesson 13: Find areas by decomposing into rectangles or completing composite figures to form rectangles.

Name Date

1. Each of the following figures is made up of 2 rectangles. Find the total area of each figure.

Figure 1: Area of A + Area of B: _________ + _________ = _________ sq units

Figure 2: Area of C + Area of D: _________ + _________ = _________ sq units

Figure 3: Area of E + Area of F: _________ + _________ = _________ sq units

Figure 4: Area of G + Area of H: _________ + _________ = _________ sq units

A

B

C

D

E F

G

H

Figure 1

Figure 2

Figure 3

Figure 4

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2. The figure shows a small rectangle cut out of a big rectangle. Find the area of the shaded figure.

3. The figure shows a small rectangle cut out of a big rectangle.

Area of the shaded figure: ______ – ______ = ______ sq cm

3 cm

3 cm

8 cm

7 cm

a. Label the missing measurements.

b. Area of the big rectangle: ______ × ______ = ______ sq cm

c. Area of the small rectangle: ______ × ______ = ______ sq cm

d. Find the area of the shaded figure.

6 cm

_____ cm

4 cm

9 cm

_____ cm

8 cm

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Lesson 14 Homework

3 4


Name Date

1. Find the area of each of the following figures. All figures are made up of rectangles.

a.

b.

8 feet

3 feet

6 feet 3 feet

5 inches

3 inches

4 inches 2 inches

8 inches

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Lesson 14 Homework

3 4


2. The figure below shows a small rectangle cut out of a big rectangle.

a. Label the side lengths of the unshaded region.

b. Find the area of the shaded region.

7 feet 3 feet 2 feet

2 feet

2 feet

10 feet

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Lesson 15: Apply knowledge of area to determine areas of rooms in a given floor plan.

Name Date

Use a ruler to measure the side lengths of each lettered room in centimeters. Then, find the area. Use the measurements below to match, and label the rooms with the correct areas.

Kitchen: 45 square centimeters Living Room: 63 square centimeters

Porch: 34 square centimeters Bedroom: 56 square centimeters

Bathroom: 24 square centimeters Hallway: 12 square centimeters

1 2

3

4

5

6

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Lesson 16: Apply knowledge of area to determine areas of rooms in a given floor plan.

Name Date

Jeremy plans and designs his own dream playground on grid paper. His new playground will cover a total area of 72 square units. The chart shows how much space he gives for each piece of equipment, or area. Use the information in the chart to draw and label a possible way Jeremy can plan his playground.

Basketball court 10 square units

Jungle gym 9 square units

Slide 6 square units

Soccer area 24 square units

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Documents

Multiplication and Area - Ms. vecore's third grade...3•Lesson 2 Homework 4 Lesson 2: Decompose and recompose shapes to compare areas. Name Date 1. Each is a square unit. Count to